2018-05-25T00:10:14Zhttp://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=8592011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Autobiography of Mircea V. DiudeaM.DIUDEA2011040115http://ijmc.kashanu.ac.ir/article_5132_542962ee079744a160a8f465da981586.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Hyperdiamonds: a Topological ViewM.DIUDEAA.ILIĆM.MEDELEANUHyperdiamonds are covalently bonded fullerenes in crystalline forms, more or less related to diamond, and having a significant amount of sp3 carbon atoms. Design of several hypothetical crystal networks was performed by using our original software programs CVNET and NANO-STUDIO. The topology of the networks is described in terms of the net parameters and several counting polynomials, calculated by NANO-STUDIO, OMEGA and PI software programs.HyperdiamondCrystal-like networkMolecular topologyCounting polynomial20110401729http://ijmc.kashanu.ac.ir/article_5162_9974b6f2617e306680ac7ca9131b449a.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Evaluation of the Mineral Contents in Fish Meal by FT- NIR using PLS and Kernel PLSS.MASOUMA.ALISHAHIM.SHEKARCHIH.FARAHMANDIn the present work we study the use of Fourier transform near infrared spectroscopy (FTNIRS) technique to analysis the calcium (Ca), phosphorus (P) and copper (Cu) contents of fish meal. The regression methods employed were partial least squares (PLS) and kernel partial least squares (KPLS). The results showed that the efficiency of KPLS was better than PLS. As a whole, the application of FT-NIRS with PLS and KPLS was as a suitable option for replacing the routine chemical analysis to assess the mineral content in fish meal, allowing immediate control of the fish meal without prior sample treatment or destruction.CalciumPhosphorusCopperFish mealFT-NIRSKPLS201104013138http://ijmc.kashanu.ac.ir/article_5163_28dfda8b8cd531f153602fa22ca08baa.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Eccentric and Total Eccentric Connectivity Indices of CaterpillarsKH.FATHALIKHANIH.YOUSEFI-AZARIConsider a simple connected graph 􀜩 with the vertex set 􀜸􁈺􀜩􁈻. The eccentric and total connectivity indices of 􀜩 are defined as 􀟦􀯖􁈺􀜩􁈻 􀵌 Σ􀯩􀗐􀜸􁈺􀜩􁈻 􀝁􀜿􀯀􁈺􀝒􁈻􀝀􀝁􀝃􀯀􁈺􀝒􁈻 and 􀜧􀜥􁈺􀜩􁈻 􀵌 Σ􀯩􀗐􀜸􁈺􀜩􁈻 􀝁􀜿􀯀􁈺􀝒􁈻, respectively. Here, 􀝀􀝁􀝃􀯀􁈺􀝒􁈻 denotes the degree of a vertex 􀝒 and 􀝁􀜿􀯀􁈺􀝒􁈻 is its eccentricity. In this paper, these two indices are calculated for a given arbitrary caterpillar.eccentric connectivity indexTotal eccentricity indexCaterpillar201104013944http://ijmc.kashanu.ac.ir/article_5164_5eab17f138e0f73210f23c5b0adcbc49.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Energy and Wiener Index of Zero-Divisor GraphsM.AHMADIR.JAHANI-NEZHADLet R be a commutative ring and (R) be its zerodivisor graph. In this article, we study Wiener index and energy of Γ(Zn ) where n = pq or n = p2q and p, q are primes. A MATLAB code for our calculations is also presented.zero-divisor graphEnergyWiener index201104014551http://ijmc.kashanu.ac.ir/article_5166_d13709db3d3b7a37193dd283d8f6696f.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)The Clar Number of Fullerene C24n and Carbon Nanocone CNC4[n]M.GHORBANIE.NASERPOURA fullerene graph is a 3−connected planar graph whose faces are pentagons and hexagons. The Clar number of a fullerene is the maximum size of sextet patterns, the sets of disjoint hexagons which are all M-alternating for a Kekulé structure M of F. An exact formula of Clar number of some fullerene graphs and a class of carbon nanocones are obtained in this paper.FullereneClar numberSextet patternCarbon nanotubeKekulé structure201104015359http://ijmc.kashanu.ac.ir/article_5168_497b64ea009a4954544694dc1fdc09b7.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)The Eccentric Connectivity Index of Some Special GraphsM.IRANMANESHR.HAFEZIEHIf 􀜩 is a connected graph with vertex set 􀜸, then the eccentric connectivity index of 􀜩, 􀣈􀡯􁈺􀜩􁈻, is defined as Σ􀯩􀗐􀯏 deg􁈺􀝒􁈻 􀝁􀜿􀜿􁈺􀝒􁈻 where deg 􁈺􀝒􁈻 is the degree of a vertex 􀝒 and 􀝁􀜿􀜿􁈺􀝒􁈻 is its eccentricity. Let A, B and C are families of graphs made by joining 􀜲􀯡 to 􀜭􀯠, made by putting 􀜭􀯠instead of each vertex in 􀜲􀯡 and made by putting 􀜥􀯠 instead of each vertex in 􀜲􀯡, respectively. In this paper we compute the eccentric connectivity index of these families of graphs.eccentric connectivity indexgraph201104016165http://ijmc.kashanu.ac.ir/article_5169_5b44cd85146f77aa944ddc562bf0add2.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Further Results on Wiener Polarity Index of GraphsA.BEHMARAMH.YOUSEFI-AZARIThe Wiener polarity index Wp(G) of a molecular graph G of order n is the number of unordered pairs of vertices u, v of G such that the distance d(u,v) between u and v is 3. In an earlier paper, some extremal properties of this graph invariant in the class of catacondensed hexagonal systems and fullerene graphs were investigated. In this paper, some new bounds for this graph invariant are presented. A relationship between Wiener and Wiener polarity index of some classes of graphs are also presented.Fullerene graphWiener indexWiener polarity index201104016770http://ijmc.kashanu.ac.ir/article_5170_ec5326da713aad93a04c35d905351ba2.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Hosoya Polynomial of an Infinite Family of Dendrimer NanostarCH.ESLAHCHIS.ALIKHANIM.AKHBARILet G be a simple graph. The Hosoya polynomial of G is ( , ) , ( , ) = { , } ( ) xd u v H G x  u v V G where d(u,v) denotes the distance between vertices u and v . The dendrimer nanostar is a part of a new group of macromolecules. In this paper we compute the Hosoya polynomial for an infinite family of dendrimer nanostar. As a consequence we obtain the Wiener index and the hyper-Wiener index of this dendrimer.Hosoya polynomialWiener indexDendrimer nanostardiameter201104017179http://ijmc.kashanu.ac.ir/article_5171_d7afdc71a1f11f23e5c5555ed15965bf.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)On the Spectra of Reduced Distance Matrix of Thorn GraphsA.HEYDARILet G be a simple connected graph and {v1, v2, …, vk} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)– entry is the topological distance between vi and vj of G. In this paper, we obtain the spectrum of the reduced distance matrix of thorn graph of G, a graph which obtained by attaching some new vertices to pendent vertices of G. As an application we compute the spectrum of reduced distance matrix for some dendrimer graphs.Reduced distance matrixspectrumThorn graphDendrimer graphs201104018187http://ijmc.kashanu.ac.ir/article_5172_53f42679383c642229cfeea0f630e490.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)On the General Sum–Connectivity Co–Index of GraphsG.SUL.XUIn this paper, a new molecular-structure descriptor, the general sum–connectivity co–index   is considered, which generalizes the first Zagreb co–index and the general sum– connectivity index of graph theory. We mainly explore the lower and upper bounds in terms of the order and size for this new invariant. Additionally, the Nordhaus–Gaddum–type result is also represented.General sum–connectivity co–indexFirst Zagreb co–indexLower and upper bounds201104018998http://ijmc.kashanu.ac.ir/article_5173_d154da6922ebac74f4671c7b5af8d008.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Distance Property of FullerenesA.GRAOVACO.ORIM.FAGHANIA.ASHRAFIFullerenes are closed−cage carbon molecules formed by 12 pentagonal and n/2 – 10 hexagonal faces, where n is the number of carbon atoms. Patrick Fowler in his lecture in MCC 2009 asked about the Wiener index of fullerenes in general. In this paper we respond partially to this question for an infinite class of fullerenes with exactly 10n carbon atoms. Our method is general and can be applied to fullerene graphs with centrosymmetric adjacency matrix.FullereneWiener indexCentrosymmetric matrix2011040199107http://ijmc.kashanu.ac.ir/article_5174_a4f7e3d101aca42bffedccebfe768ede.pdf2011-04-0110.22052Iranian Journal of Mathematical ChemistryIranian J. Math. Chem.2228-64892228-648920112Issue 1 (Special Issue on the Occasion of Mircea V. Diudea's Sixtieth Birthday)Computing Some Topological Indices of Tensor Product of GraphsZ.YARAHMADIA topological index of a molecular graph G is a numeric quantity related to G which is invariant under symmetry properties of G. In this paper we obtain the Randić, geometricarithmetic, first and second Zagreb indices , first and second Zagreb coindices of tensor product of two graphs and then the Harary, Schultz and modified Schultz indices of tensor product of a graph G with complete graph of order n are obtained.Topological indextensor product20110401109118http://ijmc.kashanu.ac.ir/article_5175_c563e2473a6d4006667114ee0582be34.pdf